Abstract
The longwave phenomenological model is used to make simple and precise calculations of various physical quantities such as the vibrational energy density, the vibrational energy, the relative mechanical displacement, and the one-dimensional stress tensor of a porous silicon distributed Bragg reflector. From general principles such as invariance under time reversal, invariance under space reflection, and conservation of energy density flux, the equivalence of the tunneling times for both transmission and reflection is demonstrated. Here, we study the tunneling times of acoustic phonon packets through a distributed Bragg reflector in porous silicon multilayer structures, and we report the possibility that a phenomenon called Hartman effect appears in these structures.
Highlights
Phonons, the quanta of lattice vibrations, manifest themselves practically in all electrical, thermal, and optical phenomena in semiconductors and other material systems
Let us consider that the phonon propagation is normal to the layer interfaces and adopt the continuum model valid for long-wavelength oscillations
In this paper, we studied tunneling times of acoustic phonon packets through a distributed Bragg reflector made of porous silicon layers
Summary
The quanta of lattice vibrations, manifest themselves practically in all electrical, thermal, and optical phenomena in semiconductors and other material systems. The reduction of the size of electronic devices below the acoustic phonon mean free path creates a new situation for phonon propagation and interaction, opening up an exciting opportunity for engineering phonon spectrum in nanostructured materials [1]. Since the early work of Narayanamurti et al [2], important progress has lately emerged in the development of nanowave phononic devices including, e.g., mirrors, cavities, and monochromatic sources. The Hartman effect (HE) states that the tunneling time becomes independent of the barrier length [4]. The independence of tunneling time on barrier length would imply arbitrarily large and superluminal velocities for tunneling wave packets, if tunneling was a propagation phenomenon
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